Minarchy is real ... it has a funny name, yes, but it's real ... It's basically a system of minimal government, probably agreeing in most respects with libertarianism. Wikipedia considers it to just be a subset of libertarianism, but my understanding is that minarchy is a futuristic goal, rather like Communism is a goal, whereas libertarianism is a political ideology that can be put into place immediately.

Rule by King Minos. By extension, a rule characterized by a labyrinthine system of taxation (Can I claim the Athenian youth deduction?) and a very … particular attraction to certain prize bulls.

To be fair, I'm not sure Minos necessarily approved of his wife's attitude toward bulls...

[Trivia: the ancient Greeks believed death was indeed a Minarchy of this kind. They believed that after death the souls of the dead were judged, and delivered to elysium or hades, by the three dread judges of the soul. These were Aeacus and Rhadamanthys, who held rods of authority, and Minos, who sat above them and held a golden sceptre. It's therefore ultimately Minos who acts as the final judge for all the dead.]

Regarding the other sense of 'minarchy': I've sometimes seen it used, for a Nozickian system of government, though I don't think Nozick actually used the word. [He said things like "the minimal state" instead]. I would say that "libertarianism" is a description of values, priorities and the moral requirements that any just system of government must meet; whereas "minarchism", in the sense of Nozickian minimal-state libertarianism, is a specific constitutional model - a theory about what sort of government could meet the requirements of libertarianism.

There are essentially four political questions in life:
- what are the criteria of a just state?
- what sort of state could meet those criteria?
- what strategies can best bring about that sort of state?
- what policies best serve those strategies at the current place and time?

For instance, a modern communist might say:
- the only just state is one without class exploitation
- class exploitation can only be avoided in a classless society with communal ownership of the means of production
- such a society can only be achieved through a vanguard-led revolution that establishes a temporary dictatorship of the proletariat
- the prospects for such a revolution are best improved by inviting other students to a demonstration against the abuse employment conditions imposed by Apple on their Chinese workforce

In this scheme, "libertarianism" is a first-order theory (the only just state is one without coercive appropriation of legitimately-aquired property), and "minarchism" is a second-order theory (the just libertarian state is best instantiated by a minimal state framework, which uses coercion only to prevent certain abuses by individuals that would otherwise make the free enjoyment of property impossible). An anarchist libertarian, by contrast, would agree with the first-order theory, but would disagree at the second level, instead insisting that even a minimal state was impermissable.

The Wenthars, incidentally, have a democratic government, the constitution of which derives heavily from that of 19th century Norway.

Some oddities include:
- many laws describe the powers of the king. When the king is absent from the islands, those powers rest with the viceroy. In brief periods in which no viceroy is present either, the powers are temporarily taken up by the Speaker. However, since independence, no actual king has ever been appointed to replace the Norwegian monarchy, and therefore the temporary holding of power by the Speaker has continued for over a hundred years;
- following the Norwegian model, elections are indirect: local areas elect representatives who gather in each district to elect deputies to parliament. This voting is by block, but the result have traditionally favoured multi-party democracy, due to deal-making and coalitions at the district level;
- following the Norwegian model, the bicameralism is weak; the upper house is simply elected by the lower house, and the veto of the upper house can be overcome by a vote of both houses together;
- the Speaker sits in both houses
- the Speaker nominates a Council of State who are not (or must resign from being) deputies in parliament. All government actions are performed by the relevent minister of state; however, the Speaker can dismiss the minister at will.